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Chapter C Answers to Selected Exercises

This appendix contains answers to all non-WeBWorK exercises in the text. For WeBWorK exercises, please use the HTML version of the text for access to answers and solutions.

Chapter 1 Understanding the Derivative

Section 1.1 How do we measure velocity?

Subsection Exercises

Section 1.2 The notion of limit

Subsection Exercises

Section 1.3 The derivative of a function at a point

Subsection Exercises

Section 1.4 The derivative function

Subsection Exercises

Section 1.5 Interpreting, estimating, and using the derivative

Subsection Exercises

Section 1.6 The second derivative

Subsection Exercises

Section 1.7 Limits, Continuity, and Differentiability

Subsection Exercises

Section 1.8 The Tangent Line Approximation

Subsection Exercises

Chapter 2 Computing Derivatives

Section 2.1 Elementary derivative rules

Subsection Exercises

Section 2.2 The sine and cosine functions

Subsection Exercises

Section 2.3 The product and quotient rules

Subsection Exercises

Section 2.4 Derivatives of other trigonometric functions

Subsection Exercises

Section 2.5 The chain rule

Subsection Exercises

Section 2.6 Derivatives of Inverse Functions

Subsection Exercises

Section 2.7 Derivatives of Functions Given Implicitly

Subsection Exercises

Section 2.8 Using Derivatives to Evaluate Limits

Subsection Exercises

Chapter 3 Using Derivatives

Section 3.1 Using derivatives to identify extreme values

Subsection Exercises

Section 3.2 Using derivatives to describe families of functions

Subsection Exercises

Section 3.3 Global Optimization

Subsection Exercises

Section 3.4 Applied Optimization

Subsection Exercises

Section 3.5 Related Rates

Subsection Exercises

Chapter 4 The Definite Integral

Section 4.1 Determining distance traveled from velocity

Subsection Exercises

Section 4.2 Riemann Sums

Subsection Exercises

Section 4.3 The Definite Integral

Subsection Exercises

Section 4.4 The Fundamental Theorem of Calculus

Subsection Exercises

Chapter 5 Evaluating Integrals

Section 5.1 Constructing Accurate Graphs of Antiderivatives

Subsection Exercises

Section 5.2 The Second Fundamental Theorem of Calculus

Subsection Exercises

Section 5.3 Integration by Substitution

Subsection Exercises

Section 5.4 Integration by Parts

Subsection Exercises

Section 5.5 Other Options for Finding Algebraic Antiderivatives

Subsection Exercises

Section 5.6 Numerical Integration

Subsection Exercises

Chapter 6 Using Definite Integrals

Section 6.1 Using Definite Integrals to Find Area and Length

Subsection Exercises

Section 6.2 Using Definite Integrals to Find Volume

Subsection Exercises

Section 6.3 Density, Mass, and Center of Mass

Subsection Exercises

Section 6.4 Physics Applications: Work, Force, and Pressure

Subsection Exercises

Section 6.5 Improper Integrals

Subsection Exercises

Chapter 7 Differential Equations

Section 7.1 An Introduction to Differential Equations

Subsection Exercises

Section 7.2 Qualitative behavior of solutions to DEs

Subsection Exercises

Section 7.3 Euler's method

Subsection Exercises

Section 7.4 Separable differential equations

Subsection Exercises

Section 7.5 Modeling with differential equations

Subsection Exercises

Section 7.6 Population Growth and the Logistic Equation

Subsection Exercises

Chapter 8 Sequences and Series

Section 8.1 Sequences

Subsection Exercises